New Jersey has settled a legal dispute with a contractor that was dismissed over its work helping homeowners rebuild from superstorm Sandy, the conclusion of a troublesome chapter in the state’s efforts to help thousands of displaced residents rebuild from the 2012 storm.

The office of Acting Attorney General John Hoffman settled the 13-month dispute with Hammerman & Gainer Inc., a Louisiana-based firm known as HGI, on Thursday. The state has agreed to pay $7.6 million in outstanding invoices, or about a third of the $22 million that the company had been seeking from state taxpayers, according to the 10-page agreement.

In total, the company received more than $43 million from the state as part of a contract originally valued at $68 million.

The settlement includes payments for operating housing recovery centers, website administration, travel expenses and a call center for homeowners seeking assistance to rebuild their homes after the October 2012 storm devastated the region.

Sandy, one of the costliest storms in U.S. history, damaged about 200,000 homes from New Jersey to eastern Long Island, N.Y., while killing 87 people in the area.

Lisa Ryan, a spokeswoman for the state Department of Community Affairs, the agency running New Jersey’s Sandy housing recovery programs, said the settlement allows the state “to continue our focus on getting Sandy-impacted families back in their homes.”

In a statement, HGI called the settlement “amicable” and that the company still stands by its work in New Jersey.

“The decision to resolve this dispute was strictly a business decision to allow HGI to put an end to protracted and costly litigation and focus on other projects,” the company’s lawyer said.

Officials at housing groups that criticized Gov. Chris Christie’s handling of the storm said the settlement precludes a full public airing of the complaints about HGI’s performance.

“People who are still out of their homes still don’t know why they received such poor treatment,” said Kevin Walsh of the Fair Share Housing Center, an advocacy group that sued the administration over its handling of federal Sandy funds.

The state faulted HGI for subpar work, while company officials previously said New Jersey changed the rules so frequently that it couldn’t perform its job.

The settlement doesn’t render any assessment of fault in the dispute. It effectively ended New Jersey’s relationship with HGI, unless federal officials turn up irregularities as part of an audit of the state’s use of taxpayer funds.

Sandy severely damaged more than 40,000 homes in New Jersey, according to federal estimates. Federal officials have approved $3.3 billion for the state to rebuild its housing stock.

HGI was hired as a contractor in 2013 to help Sandy victims apply for grants associated with New Jersey’s largest recovery effort for homeowners, an initiative known as the “Reconstruction, Rehabilitation, Elevation and Mitigation Program.” This program awards grants of up to $150,000 for victims to rebuild their primary homes.

As of last month, the state had signed grants with 6,800 applicants, amounting to $838 million in funding, state figures show.

Many grant applicants had complained about the program’s administration under HGI. The complaints included charges of lost applications and inadequately trained case managers.

“Those early days were a nightmare,” said Joe Mangino, a Beach Haven West resident and grant applicant who has yet to return to his damaged home. “I almost felt like they were doing it on purpose to make me go away.”

State officials acknowledged in testimony before lawmakers and in response to a story by The Wall Street Journal that HGI wasn’t meeting the government’s expectations in serving those seeking Sandy assistance

The firm’s contract was severed in January 2014. At that point, the state had paid the company $36 million.

Both sides had mutually agreed to part ways, but in April of last year HGI sought $22 million from the state for outstanding invoices.

The parties tried to resolve the matter through arbitration but those discussions failed, with each side exchanging angry accusations.

This week’s settlement included about $354,000 in travel costs for the firm to perform its work in New Jersey. New Jersey succeeded in disputing $38,000 in travel expenses, according to the agreement.

State officials characterized the settlement as a win for New Jersey, as government lawyers were able to substantially reduce HGI’s financial claims.

But some residents, such as Mr. Mangino, said they are very displeased because the company shouldn’t be paid a penny more.

“It makes me furious to be honest with you,” Mr. Mangino said.

After the state parted ways with HGI, New Jersey began relying on another contractor, ICF International, to perform administrative functions over its Sandy program. The Virginia-based company has been paid $26 million through December, according to the most recent state report.

New Jersey has spent $150 million on contractors assisting with the housing recovery through the end of last year, according to the most recent available figures.

In recent months, state employees have taken over more of the administration of Sandy housing programs, reducing the government’s reliance on outside contractors, officials said.

“DCA is investing the time, energy and resources necessary to overcome Sandy recovery challenges and we look forward to continuing to help families with their individual rebuilding efforts,” Ms. Ryan said.